A pattern has 5 blue triangles to every 80 yellow triangles. What is the ratio of blue triangles to all triangles?

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

Un carpintero quiere cortar una plancha de triple y de 1m de largo y 60 cm de ancho, en cuadrados lo más grandes posibles. El ca

Ugo [173]

Answer: $20\ cm$

Step-by-step explanation:

The first step to solve the exercise is to make the conversion from meters to centimeters.

Since $1\ m=100\ cm$ , then the dimensions of the wood board in centimeters are:

$Lenght=100\ cm\\\\Width=60\ cm$

Now, you must find the Greatest Common Factor (GCF). The steps are:

- Descompose 100 and 60 into their prime factors:

$100=2*2*5*5=2^2*5^2\\60=2*2*3*5=2^2*3*5$

- Multiply the commons with the lowest exponents:

$GCF=2^2*5\\\\GCF=4*5\\\\GCF=20$

Therefore, the side lenght of each square must be:

$s=20\ cm$

7 0

3 years ago

Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gem

Finger [1]

Answer:

10.2 grams

Step-by-step explanation:

Gemma had 25.75 grams of frosting

Used 15.5 grams

Left over:

25.75 - 15.5 = 10.2 grams

8 0

3 years ago

3. Name the angles from largest to smallest

Scilla [17]

Answer:

largest to smallest is.

Step-by-step explanation:

hope this helps

5 0

3 years ago

A bag contains 40 marbles. The probability of selecting a red marble at random is 1/5. How many red marbles are in the bag?

goblinko [34]

Answer:

8 red marbles.

Step-by-step explanation:

All together we have 40 marbles. The fraction of marbles that are red is 1/5 which means that we should divide the total number of marbles, which is 40 by the denominator ( Bottom number of fraction ) 5 so that we get the number of groups that have 1 red marble in them. In this case we have 8 groups.

40/5=8

You always divide by the denominator ( Bottom number of fraction ) first and then you multiply your answer by the numerator ( Top number of fraction ) .

If each group has 1 red marble in it and we have 8 groups, it means that we have 8 red marbles in the bag.

1 * 8 = 8 red marbles in the bag

If the numerator (number above the fraction line) was more than one, then this would mean that we have more than 1 marble in each group of marbles.

Example:

If we had 3/5 we would have 3 marbles in each group of marbles. This means that instead of doing 1 * 8 we would have to do 3 * 8 = 24. We would have 24 red marbles in the bag.

Easy and quick way if you do not need the explanation:

Another way we could do this is by simply multiplying the fraction ( 1/5 ) by the total number of marbles ( 40 ). This would still give us an answer of 8 red marbles in the bag. 40/5=8, 8*1=8

7 0

3 years ago